Title: Stability results for the Gross-Pitaevskii equation
Abstract: Gross-Pitaevskii is a dispersive equation that describes the behavior of superluids and superconductors. Its dispersive estimates are worse than those for Schrödinger, which leads to difficulties when studying the stability problems. In this talk, we present recent progress on these questions, in particular concerning the stability of vortices, which are stationary solutions of this equation.